On the colored Jones polynomials of certain cable of the torus knots

TL;DR

This paper investigates the asymptotic behavior of colored Jones polynomials at roots of unity for specific knots, confirming the volume conjecture's prediction that certain limits tend to zero.

Contribution

It provides new evidence supporting the volume conjecture for a class of cable torus knots by analyzing their colored Jones polynomials.

Findings

Limit of colored Jones polynomials at roots of unity is zero for the studied knots.

Supports the volume conjecture in the context of cable torus knots.

Abstract

In this paper, we study the asymptotic behavior of the colored Jones polynomials evaluated at roots of unity for a special class of knots. We show that certain limit is zero as predicted by the volume conjecture.